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Intel stock investors received the company's quarterly earnings report last month, and things went about as expected, which wasn't great. Net income was down 17% and revenue was down 7% from the previous quarter. But aside from Intel's numbers, the company is in a battle for mobile relevance, and there are three key areas investors should be specifically watching:

New leadership With the announcement back in November that CEO Paul Otellini was unexpectedly resigning after holding the position since 2005, the company began its search to find a replacement rather suddenly. Just a few days ago, Intel's chief operating officer, Brian Krzanich, was named the CEO, an unsurprising move for a company that always picks its top leader from within, and usually from the COO position.

The company is changing leadership at a critical moment in its history, which could be a good or bad thing. Intel desperately needs to transition further into mobile and Krzanich may help tip the company in the right direction. Although hiring Krzanich as CEO is less likely to make any waves within the company, investors need to keep an eye on things. Krzanich has been with the company for thirty years, so that offer stability, but Intel desperately needs to move forward in mobile.

Building on current relationshipsYou don't become the No. 1 semiconductor company without making some great connections, and Intel has plenty of them. Although the PC market declined 14% in the Q1 2013 -- read: bad news for Intel -- the company is still makes processors for one of the only companies doing well in the PC market: Apple .

Some have suggested that Intel may be able to strike a deal for mobile processors with Apple, but nothing has solidified yet. With Krzanich's strong manufacturing background, and Intel building processors for a growing number of chip makers, it might be the best time to make Apple an offer it can't refuse.

On the mobile side, Intel is a founding member of Samsung's new operating system initiative, Tizen. Samsung is looking to pull away from Google's Android, and Tizen may be the way to do it. The company announced last month that the first Tizen high-end smartphone will launch in August or September. Intel is likely the maker of the Tizen processors, and if additional OEMs jump on board with the OS, as Intel expects them to, then the company would be smack dab in the middle of mobile pretty quickly. Tizen will have a significant uphill battle on its hands, considering Google and Apple's OS market share, but with mobile powerhouse Samsung pushing the project, it may just have a real chance.

The competition The last (but not least) thing Intel stock investors need to watch is how the company combats its competition. In the baseband market, Qualcomm dominates with 52% of the market share, MediaTek takes 12.5%, and Intel comes in No. 3 with 12.3%. In addition, Intel is behind the eight ball when it comes to LTE chips. Qualcomm has a dual-mode LTE chip -- allowing for both voice and data signals -- while Intel plans to launch a dual-mode chip in the first half of this year.

Both Qualcomm and NVIDIA have application processors with integrated LTE capabilities built on top of them, a growing standard for mobile devices. But Intel won't have similar chips available until sometime in 2014. Things move quickly in the mobile space, and falling behind Qualcomm, NVIDIA, and MediaTek doesn't bode well for the company.

To top it all off, ARM Holdings , whose chip design technology can be found in most mobile devices, is creeping into one of Intel's core businesses: server microprocessors. ARM became the go-to chip designer for mobile with its low power consumption and high-performance output technology, while Intel fell behind. Intel has been fighting to catch up with ARM in the mobile arena, but now it seems it will have to fight off the company for its once-safe server processor market as well.

Mobile or bustThough PCs sales are on the decline, Intel can still make money from its PC and server processor business as it moves further into mobile. But the company needs to move fast and turn its mobile prospects into real revenue generators. Many of the company's competitors already have a jump on Intel, and stock investors can't wait much longer for Intel to get mobile right.

When it comes to dominating markets, it doesn't get much better than Intel's position in the PC microprocessor arena. However, that market is maturing, and Intel finds itself in a precarious situation longer term if it doesn't find new avenues for growth. In this premium research report on Intel, a Motley Fool analyst runs through all of the key topics investors should understand about the chip giant. Click here now to learn more.

Fool contributor Chris Neiger has no position in any stocks mentioned. The Motley Fool recommends Apple, Google, Intel, and NVIDIA. The Motley Fool owns shares of Apple, Google, Intel, and Qualcomm. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.